Theory of combined action

In their design it is necessary to take into account the combined action of fiber and resin. Sometimes the combination can be considered to be homogeneous and, therefore, to be similar to engineering materials like metal but in other cases, homogeneity cannot be assumed and it is necessary to take into account the fact that two widely dissimilar materials have been combined into a single unit. 

In designing these reinforced plastics, certain important assumptions are made. The first and most fundamental is that the two materials act together and that the stretching, compression, and twisting of fibers and of resin under load is the same, that is, the strains in fiber and resin are equal. This assumption implies that a good bond exists between resin and fiber to prevent slippage between them and to prevent wrinkling of the fiber. 

The second major assumption is that the material is elastic, that is, strains are directly proportional to the stresses applied, and when a load is removed the deformation disappears. In engineering terms the material is assumed to obey Hooke s Law. This assumption is probably a close approximation of the actual behavior in direct stress below the proportional limit, particularly in tension, if the fibers are stiff and elastic in the Hookean sense and carry essentially all of the stress. The assumption is probably less valid in shear where the resin carries a substantial portion of the stress. The resin may undergo plastic flow leading to creep or to relaxation of stress, especially when stresses are high. 

More or less implicit in the theory of materials of this type is the assumption that all of the fibers are straight and unstressed or that the initial stresses in the individual fibers are essentially equal. In practice it is quite unlikely that this is true. It is to be expected, therefore, that as the load is increased some fibers reach their breaking points first. As they fail, their loads are transferred to other as yet unbroken fibers, with the consequence that failure is caused by the successive breaking of fibers rather than by the simultaneous breaking of all of them. The 

Design theory shows that the values of a number of elastic constants must be known in addition to the strength properties of the resin, fibers, and combination. Reasonable assumptions are made in carrying out designs. In the examples used, more or less arbitrary values of elastic constants and strength values have been chosen to illustrate the theory. Any other values could be used. 

---

Orientation of reinforcement The behavior of RPs is dominated by the arrangement and the interaction of the stiff, strong fibers with the less stiff, weaker plastic matrix. The features of the structure and the construction determine the behavior of RPs that is important to the designer. A major advantage is the fact that directional properties can be maximized in the plane of the sheet. As shown in Fig. 8-55 they can be isotropic, orthotropic, etc. Basic design theories of combining actions of plastics and reinforcements... 

The first indication of the existence of a captodative substituent effect by Dewar (1952) was based on 7t-molecular orbital theory. The combined action of the n-electrons of a donor and a captor substituent on the total Jt-electron energy of a free radical was derived by perturbation theory. Besides the formulation of this special stabilizing situation and the quotation of a literature example [5] (Goldschmidt, 1920, 1929) as experimental evidence, the elaboration of the phenomenon was not pursued further, neither theoretically nor experimentally. 

The ES complex is the key to understanding this kinetic behavior, just as it was a starting point for our discussion of catalysis. The kinetic pattern in Figure 6-11 led Victor Henri, following the lead of Wurtz, to propose in 1903 that the combination of an enzyme with its substrate molecule to form an ES complex is a necessary step in enzymatic catalysis. This idea was expanded into a general theory of enzyme action, particularly by Leonor Michaelis and Maud Menten in 1913. They postulated that the enzyme first combines reversibly with... 

Paton, W. D. M. A Theory of Drug Action Based on the Rate of Drug-Receptor Combination. Proc. R. Soc. London, Ser. B. 1961,154, 21-69. 

This mechanism was defined later by Bush [6] as the blocking mechanism. Bush s classification is based on Raton s rate theory of drug action [181]. Raton suggested that a pharmacological effect depends not upon the number of individual drug-receptor combinations but upon the rate, of drug-receptor occupation. He assumes that receptor... 

Enzymes are proteins that act as catalysts for specific biochemical reactions in living systems. The reactants in enz)une-catalyzed reactions are called substrates. Thousands of vital processes in our bodies are catalyzed by many distinct enzymes. For instance, the enzyme carbonic anhydrase catalyzes the combination of CO2 and water (the substrates), facilitating most of the transport of carbon dioxide in the blood. This combination reaction, ordinarily uselessly slow, proceeds rapidly in the presence of carbonic anhydrase a single molecule of this enzyme can promote the conversion of more than 1 million molecules of carbon dioxide each second. Each enzyme is extremely specific, catalyzing only a few closely related reactions—or, in many cases, only one particular reaction—for only certain substrates. Modern theories of enzyme action attribute this to the requirement of very specific matching of shapes (molecular geometries) for a particular substrate to bind to a particular enzyme (Figure 16-19). 

Paton, W. D. M. (1961). A theory of drug action based on the rate of drug-receptor combinations. Proceeding of the Royal Society of London, Series B, 154, 21—69. 

An interesting theory of promoter action is based on the belief that interfaces are the seat of catalytic activity—the active centers.1,2 It is apparent that new boundaries will be provided and existing ones altered when one solid is incorporated with another, and the enhanced activity may reside in specific configurations produced at boundaries of the two solids. That boundaries between surfaces can be the seat of activity is supported by the fact that a decomposition or combination may be difficult to start on a solid surface consisting entirely of a single component. Overburnt lime does not hydrate readily because water does not combine except where hydration has already begun.22 Faraday found that hydrated salts do not commence to effloresce unless the surface is scratched. The action of manganese dioxide on the decomposition of potassium... 

W. Henry gives a good summary of BerthoUet s theory of mass action and combination in indefinite proportions and raises five objections against it ... 

The fact that one eqnation can represent, albeit qualitatively, the apparently very different foam volnme against time plots shown in both Eigures 6.15 and 6.16 could indicate that the same phenomenon underlies both sets of results. The huge difference in the valnes of m for these two plots in the main derives from a combination of enormons differences in antifoam effectiveness and a probable large difference in bubble sizes (where, as we have described in Section 5.2, a statistical theory of antifoam action predicts that larger babbles are likely to require a smaller concentration of antifoam to effect mptnre). 

This discussion refers to external plasticization only. Several theories, varyiag ia detail and complexity, have been proposed ia order to explain plasticizer action. Some theories iavolve detailed analysis of polarity, solubiHty, and iateraction parameters and the thermodynamics of polymer behavior, whereas others treat plasticization as a simple lubrication of chains of polymer from each other, analogous to the lubrication of metal parts by oil. Although each theory is not exhaustive, an understanding of the plasticization process can be gained by combining ideas from each theory, and an overall theory of plasticization must include all these aspects. 

Hence, for two similarly charged surfaces in electrolyte, interactions are determined by both electrostatic doublelayer and van der Waals forces. The consequent phenomena have been described quantitatively by the DLVO theory [6], named after Derjaguin and Landau, and Verwey and Over-beek. The interaction energy, due to combined actions of double-layer and van der Waals forces are schematically given in Fig. 3 as a function of distance D, from which one can see that the interplay of double-layer and van der Waals forces may affect the stability of a particle suspension system. 

The law of mass action has been successfully applied to many drug dose-response relationships since the early work of Clark. The systematic relation between the dose of a drug and the magnitude of its response is based on three assumptions (1) response is proportional to the level of receptor occupancy (occupancy theory), (2) one drug molecule combines with one receptor site, and (3) a negligible fraction of total drug is combined with the receptors. These assumptions must also apply to Beidler s equation. 

---